Problem: Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area. 

Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?

<image> Illustration to the first example.

Input

The first and only line of input contains two space-separated integers, n and h (2 ≤ n ≤ 1000, 1 ≤ h ≤ 105).

Output

The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold. 

Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.

Examples

Input

3 2


Output

1.154700538379 1.632993161855


Input

2 100000


Output

70710.678118654752

Note

Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class B {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		
		int n = Integer.parseInt(in.next());
		int h = Integer.parseInt(in.next());
		
		double B = 1;
		double H = h;
		
		
		double Atotal = H / 2;
		double Awanted = Atotal / n;
		double alreadyCut = 0;
		
		double[] cuts = new double[n - 1];
		
		for(int i = 0; i < n - 1; i++) {
			 double lastHguess = -1;
			 double minH = 0;
			 double maxH = H;
			 double Hguess = -2;
			 double Bguess = -2;
			 while(Hguess != lastHguess) {
			 	lastHguess = Hguess;
			 	Hguess = (minH + maxH)/2;
			 	Bguess = B * (H - Hguess) / H;
			 	double ar = area(B, Bguess, Hguess);
			 	if(ar > Awanted) {
			 		maxH = Hguess;
			 	} else {
			 		minH = Hguess;
			 	}
			 	
			 }
			 alreadyCut += Hguess;
			 H -= Hguess;
			 B = Bguess;
			 cuts[i] = alreadyCut;
		}
		
		H = h;
		for(int i = n - 2; i >= 0; i--) {
			System.out.print((H - cuts[i]) + " ");
		}
		
		System.out.println();
	}
	
	public static double area(double b1, double b2, double h) {
		return (h * (b1 + b2) / 2);
	}
	
	public static double abs(double x) {
		if(x > 0) {
			return x;
		} else {
			return x * -1;
		}
	}
}